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It may be that the soil is poor around that area. Sometimes, improving the soil by adding compost and just a little topsoil to the are can help put nutrients back into the area.

If that does not fix the issue, than it may be difficult to find anything that will grow under the tree.

Here are some articles that will offer more information on things that will grow well under trees:

https://www.gardeningknowhow.com/ornamental/trees/tgen/tips-for-growing-grass-under-a-tree.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/planting-garden-beneath-trees.htm

If these trees were removed due to disease, and it was not adequately killed off, then these trees will suffer the same fate.

It is recommended to plant a completely unrelated species, in place of something that dies, in order to prevent the disease from killing of the replacement.

Unfortunately, your new trees will likely suffer the same fate, until something new is planted.

In between, I would try solarizing the soil. This article will help:

https://www.gardeningknowhow.com/garden-how-to/projects/how-to-solarize-garden-beds-to-eliminate-garden-pests-in-the-soil.htm

I suspect it is an environmental issue due to the hot weather, but be alert to the diseases Linden trees are susceptible to. It also could be too much water. Wait till the soil starts to dry out before watering.

https://www.gardeningknowhow.com/ornamental/trees/linden/diseases-of-linden-trees.htm
https://www.gardeningknowhow.com/plant-problems/disease/verticillium-wilt-treatment.htm

Are you providing supplemental water to your tree? If not, that should help. Also prune out any dead or dying branches and twigs. Check the leaves for fungal leaf spots as well as any pests.

Here is an article about linden diseases that may help:

https://www.gardeningknowhow.com/ornamental/trees/linden/diseases-of-linden-trees.htm

Certain types of trees are prone to this. Oaks, certainly, are. Linden will be no stranger to it, as well. This happens when the lack of formation of abscission tissue occurs. Generally, this has two causes.

One is when there is sudden cold weather in autumn, which prevent the formation of abscission tissue.

The other is when the winter remains too warm for drop. This, also, prevents abscission tissue formation.

Neither will harm your trees. They will return to normal as soon as the active growing season starts.

If you lost half of it last year, I'm sure its vitality has been affected. A tree with major damage may need to be removed. Here is more:

https://www.gardeningknowhow.com/ornamental/trees/tgen/what-to-do-for-storm-damage-trees-repair.htm